Edutopia

2 years ago

in simple harmonic motion why does omega squared equal k/m? where does this come from?

This comes from the differential eqution of the harmonic motion. The model for a spring, with mass m and elastic constant k, says,
\[m\cdot a=-k x\Rightarrow m\frac{d^2x}{dt^2}+kx=0\Rightarrow \frac{d^2x}{dt^2}+\frac{k}{m}x=0\Rightarrow \frac{d^2x}{dt^2}+\omega^2x=0\]
Using the last substitution is easy to find the solution
\[x=A\cos(\omega t+\phi)\]

You can find some interesting notes about Fermi Dirac statistics in the web. For example,
http://solar.njit.edu/~leej/lecture/ph641/Ch04_summary.pdf
However, I also reommend you the Volume 5 of Berkeley Physics Course (introductory level) and the book from Kittel "Elementary Statistical Physics", Part1, Chapter 19. Other books of higher level (Hwang, Pathria) should be usefull too.